The combustion of 0.316g of benzoic acid in the same calorimeter

[zorro]

Homework Statement

A slice of banana weighing 2.502g was burnt in a bomb calorimeter producing a temperature rise of 3.05 C. The combustion of 0.316g of benzoic acid in the same calorimeter produced a tempterature rise of 3.24 C. The heat of combustion of benzoic acid at constant volume is -3227 kJ/mol. If average banana weigh 125g, how many calories can be obtained from one average banana?

Homework Equations

The Attempt at a Solution

The concept of working of a calorimeter is not clear to me. Moreover, I don't know which equation to use. Any ideas appreciated

 

[Borek]

$$q = m \times c \times \Delta T$$

However, for a calorimeter mc is constant, so you don't have to know both mass and specific heat separately, you can use total heat capacity instead.

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[zorro]

'm' is the mass of what quantity?
I read about water equivalent, mass of solution, mass of water etc.
What is the meaning of water equivalent in a calorimeter?

 

[Borek]

m is mass of a thing that changed its temperature by delta T.

 

[DeeNos]

As a scientist, the first step would be to understand the concept of a calorimeter and its working. A calorimeter is a device used to measure the heat released or absorbed during a chemical reaction. In this case, the combustion of benzoic acid and banana. The heat released during the reaction is measured by the temperature change of the surrounding water in the calorimeter.

To solve this problem, we can use the equation Q = mCΔT, where Q is the heat released, m is the mass of the substance, C is the specific heat capacity of the substance, and ΔT is the change in temperature.

First, we need to find the mass of the banana used in the calorimeter. Since the average weight of a banana is 125g, the mass of the banana used in the experiment is 2.502g/125g = 0.02g.

Using the given information, we can calculate the heat released during the combustion of the banana:

Q = (0.02g)(4.18 J/g°C)(3.05°C) = 0.25 J

Next, we can use the heat of combustion of benzoic acid (-3227 kJ/mol) to calculate the heat released during the combustion of 0.316g of benzoic acid:

Q = (0.316g)(-3227 kJ/mol) = -1020.932 kJ

Now, we can use the equation Q = mCΔT to find the specific heat capacity of the substance (benzoic acid or banana):

C = Q/(mΔT)

For the banana: C = (0.25 J)/(0.02g)(3.05°C) = 6.97 J/g°C

For benzoic acid: C = (-1020.932 kJ)/(0.316g)(3.24°C) = -1032.23 J/g°C

Since the specific heat capacity of benzoic acid is negative, it indicates that it is an exothermic reaction, releasing heat. Therefore, we can conclude that the combustion of benzoic acid releases more heat compared to the combustion of banana.

Finally, to find the number of calories obtained from one average banana, we can convert the heat released (0.25 J) into calories:

1 calorie = 4.18 J

Therefore, the number of calories obtained from one average banana is: